Graduation Year
2001
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Gregory Levin
Reader 2
Arthur Benjamin
Abstract
Tait showed in 1878 that the Four Color Theorem is equivalent to being able to three-color the edges of any planar, three-regular, two-edge connected graph. Not surprisingly, this equivalent problem proved to be equally difficult. We consider the problem of fractional colorings, which resemble ordinary colorings but allow for some degree of cheating. Happily, it is known that every planar three-regular, two-edge connected graph is fractionally three-edge colorable. Is there an analogue to Tait’s Theorem which would allow us to derive the Fractional Four Color Theorem from this edge-coloring result?
Recommended Citation
Nieh, Ari, "Fractional Analogues in Graph Theory" (2001). HMC Senior Theses. 131.
https://scholarship.claremont.edu/hmc_theses/131
Thesis Proposal
